The City of Milwaukee (WI) distinguishes between them in its new zoning code.
Here are the definitions as they have them:
"Bank or other financial institution" means an establishment providing retail banking, credit and mortgage services. This term does not include a currency exchange, a payday loan agency or a title loan agency.
"Currency exchange" means, in accordance with s. 218.05, Wis. Stats., any person except banks incorporated under the laws of this state and national banks organized pursuant to the laws of the United States and any credit union operating under ch. 186, Wis. Stats., which obtains a certificate of authority from the Wisconsin commissioner of credit unions, engaged in the business of and providing facilities for cashing checks, drafts, money orders and all other evidences of money acceptable to such community currency exchange for a fee, service charge or other consideration. This term does not include any person engaged in the business of transporting for hire, bullion, currency, securities, negotiable or nonnegotiable documents, jewels or other property of great monetary value nor any person engaged in the business of selling tangible personal property at retail nor any person licensed to practice a profession or licensed to engage in any business in this state, who in the course of such business or profession and, as an incident thereto, cashes checks, drafts, money orders or other evidences of money.
And here are a couple more related ones:
"Title loan agency" means an establishment providing loans to individuals in exchange for receiving titles to the borrowers' motor vehicles as collateral.
"Payday loan agency" means an establishment providing loans to individuals in exchange for personal checks as collateral.
Districts that permit banks don't necessarily permit currency exchanges, which appear to be more tightly restricted (based on my cursory perusal of the use tables).
For more info on Milwaukee's code, the link is:
http://www.mkedcd.org/czo/index.asp